L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 2, page 135-145
  • ISSN: 0066-2216

Abstract

top
We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.

How to cite

top

Jerzy Gawinecki. "$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity." Annales Polonici Mathematici 54.2 (1991): 135-145. <http://eudml.org/doc/262394>.

@article{JerzyGawinecki1991,
abstract = {We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the $L^p$-$L^q$-time decay estimates.},
author = {Jerzy Gawinecki},
journal = {Annales Polonici Mathematici},
keywords = {decay estimates; partial differential equations; Cauchy problem; symmetric hyperbolic system of first order; linear thermoelasticity; global existence in time},
language = {eng},
number = {2},
pages = {135-145},
title = {$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity},
url = {http://eudml.org/doc/262394},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Jerzy Gawinecki
TI - $L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 2
SP - 135
EP - 145
AB - We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the $L^p$-$L^q$-time decay estimates.
LA - eng
KW - decay estimates; partial differential equations; Cauchy problem; symmetric hyperbolic system of first order; linear thermoelasticity; global existence in time
UR - http://eudml.org/doc/262394
ER -

References

top
  1. [1] R. Adams, Sobolev Spaces, Academic Press, New York 1975. 
  2. [2] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345-392. Zbl0059.08902
  3. [3] Yu. V. Egorov, Linear Differential Equations of Principal Type, Nauka, Moscow 1984 (in Russian). 
  4. [4] J. Gawinecki, Matrix of fundamental solutions for the system of equations of hyperbolic thermoelasticity with two relaxation times and solution of the Cauchy problem, Bull. Acad. Polon. Sci., Sér. Sci. Techn. 1988 (in print). Zbl0698.73003
  5. [5] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), 43-101. Zbl0405.35056
  6. [6] S. Klainerman, Long-time behaviour of solutions to nonlinear evolution equations, Arch. Rational Mech. Anal. 78 (1982), 72-98. Zbl0502.35015
  7. [7] S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math. 36 (1983), 133-141. Zbl0509.35009
  8. [8] J. L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris 1968. Zbl0165.10801
  9. [9] A. Piskorek, Fourier and Laplace transformation with their applications, Warsaw University, 1988 (in Polish). 
  10. [10] J. Shatah, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations 46 (1982), 409-425. Zbl0518.35046
  11. [11] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, 3th ed. Nauka, Moscow 1988 (in Russian). Zbl0662.46001
  12. [12] W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-113. Zbl0466.47006
  13. [13] E. S. Suhubi, Thermoelastic solids, in: Continuum Physics, A. C. Eringen (ed.), Academic Press, New York 1975. 
  14. [14] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978. Zbl0387.46033

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.